A definition is a rethorical pattern you use to conceptualize words. Definitions usually have a term to be defined, a general class word and a characteristic or characteristics.
Example A dog (term to be defined) is an animal (general class word) that barks has four legs and a tail. (characteristics)
These are the 10 definitions I picked. Term to be defined will be underlined. General class will be in green. Characteristics will be in orange. Examples will be in fuchsia.
1) Calculus:Branch of mathematicsconcerned with rates of change, gradients of curves, maximum and minimum values of functions, and the calculation of lengths, areas and volumes. It involves determining areas (integration) and tangents (differentiation), which are mutually inverse. Also called real analysis.
2) Inverse function: A functionwhich "does the reverse" of a given function. For example, functions with the prefix arc are inverse trigonometric functions; e.g. arcsin x for the inverse of sin(x).
3) Irrational number:A real numberthat cannot be expressed as the ratio of two integers, and therefore that cannot be written as a decimal that either terminates or repeats. The square root of 2 is an example because if it is expressed as a ratio, it never gives 2 when multiplied by itself. The numbers p = 3.141592645..., and e = 2.7182818... are also irrational numbers.
4) Quadratic equation:An algebraic equationof the second degree (having one or more variables raised to the second power).The general quadratic equation is ax2 +bx + c= 0, in which a, b and c are constants (or parameters) and "a" is not equal to 0.
5) Polynomial : An algebraic expressionof the form a0xn + a1xn-1 + ... + an, where a0, a1, ..., an are members of a field (or ring), and n is the degree of the polynomial.
6) Function (f): The mathematical operationthat transforms a piece of data into a different one. For example, f(x) = x2 is a function transforming any number to its square.
7) Lowest common multiple (LCM): The smallestnon-zero natural numberthat is a common multiple of two or more natural numbers.
8) Asymptote: A straight linethat a curve approaches but never meets or crosses. The curve is said to meet the asymptote at infinity. In the equation y = 1/x, y becomes infinitely small as x increases but never reaches zero. 9) Associative property: A binary operation (*) is defined associative if, for a*(b*c) = (a*b)*c. For example, the operations addition and multiplication of natural numbers are associative, but subtraction and division are not. 10) Perfect number: A numberwhich is equal to the sum of its proper divisors. 6, 28, and 496 are the three of seven known perfect numbers. [6 is a perfect number because its proper divisors (1,2, and 3) total 6.] Great ! ! These are the 5 definitions I wrote. A square root of a real number a is another real number bwhich multiplied by itselfs equals the first one (if bxb= a , then b is a square root of a). Every real number has two different square roots, b and (-b). . A succession of numbersis a function (ak) which associates a real number to every single integrer k where the function is defined. A succesion that approaches closer and closer to a real number L from an especific integrer k is named convergent; otherwise it is called not convergent. A pair of angles are named rectangle anglesif they are both at the same side of a straight line and they are congruent. A rectangle angle measure is 90 degrees.
Substraction is a elementary arithmetic operation that substractS from a first number a second number b. It is usually said substraction is the opposite operation to addition.
The cartesian coordinates is a pair of number associated to a point in a plane. Each number indicates the position of the point using two perpendicular straight lines with a common point defined as the origin as references.
A rational number Q is a real numberthat can be described as the quotient of two other numbers, p and z, that are both integrers. If Q can be expresed as p/z, then z must be different to zero. Super Francis…
Definitions
A definition is a rethorical pattern you use to conceptualize words. Definitions usually have a term to be defined, a general class word and a characteristic or characteristics.Example
A dog (term to be defined) is an animal (general class word) that barks has four legs and a tail. (characteristics)
Assignment
1. Now select 10 definitions from the on-line mathematics dictionary at http://www.shodor.org/interactivate/dictionary/, http://www.math.com/school/glossary/glossindex.html, http://dorakmt.tripod.com/mtd/glosmath.html, or from any other math glossary or dictionary and copy them. Your job will be to identify:a. the term to be defined
b. the general class word and
c. the characteristics
2. Using your own words, write 5 definitions about any mathematical terms.
As soon as you have all these ready, please paste it in your wiki.
These are the 10 definitions I picked.
Term to be defined will be underlined.
General class will be in green.
Characteristics will be in orange.
Examples will be in fuchsia.
1) Calculus: Branch of mathematics concerned with rates of change, gradients of curves, maximum and minimum values of functions, and the calculation of lengths, areas and volumes. It involves determining areas (integration) and tangents (differentiation), which are mutually inverse. Also called real analysis.
2) Inverse function: A function which "does the reverse" of a given function. For example, functions with the prefix arc are inverse trigonometric functions; e.g. arcsin x for the inverse of sin(x).
3) Irrational number: A real number that cannot be expressed as the ratio of two integers, and therefore that cannot be written as a decimal that either terminates or repeats. The square root of 2 is an example because if it is expressed as a ratio, it never gives 2 when multiplied by itself. The numbers p = 3.141592645..., and e = 2.7182818... are also irrational numbers.
4) Quadratic equation: An algebraic equation of the second degree (having one or more variables raised to the second power).The general quadratic equation is ax2 +bx + c= 0, in which a, b and c are constants (or parameters) and "a" is not equal to 0.
5) Polynomial : An algebraic expression of the form a0xn + a1xn-1 + ... + an, where a0, a1, ..., an are members of a field (or ring), and n is the degree of the polynomial.
6) Function (f): The mathematical operation that transforms a piece of data into a different one. For example, f(x) = x2 is a function transforming any number to its square.
7) Lowest common multiple (LCM): The smallest non-zero natural number that is a common multiple of two or more natural numbers.
8) Asymptote: A straight line that a curve approaches but never meets or crosses. The curve is said to meet the asymptote at infinity. In the equation y = 1/x, y becomes infinitely small as x increases but never reaches zero.
9) Associative property: A binary operation (*) is defined associative if, for a*(b*c) = (a*b)*c. For example, the operations addition and multiplication of natural numbers are associative, but subtraction and division are not.
10) Perfect number: A number which is equal to the sum of its proper divisors. 6, 28, and 496 are the three of seven known perfect numbers. [6 is a perfect number because its proper divisors (1,2, and 3) total 6.]
Great ! !
These are the 5 definitions I wrote.
A square root of a real number a is another real number b which multiplied by itselfs equals the first one (if bxb= a , then b is a square root of a). Every real number has two different square roots, b and (-b).
.
A succession of numbers is a function (ak) which associates a real number to every single integrer k where the function is defined. A succesion that approaches closer and closer to a real number L from an especific integrer k is named convergent; otherwise it is called not convergent.
A pair of angles are named rectangle angles if they are both at the same side of a straight line and they are congruent. A rectangle angle measure is 90 degrees.
Substraction is a elementary arithmetic operation that substractS from a first number a second number b. It is usually said substraction is the opposite operation to addition.
The cartesian coordinates is a pair of number associated to a point in a plane. Each number indicates the position of the point using two perpendicular straight lines with a common point defined as the origin as references.
A rational number Q is a real number that can be described as the quotient of two other numbers, p and z, that are both integrers. If Q can be expresed as p/z, then z must be different to zero.
Super Francis…
For additional information about writing definitions, please visit the following site (this is what I printed for the class)
http://owl.english.purdue.edu/owl/resource/622/01/